330 



neglecting terms of the order of at*") we obtain 



tH - "•''. ' fr. ' (2) 



where for convenience in the subsequent discussion, the plastic frequoicy 

 has been factored into two times, a damping time ©, and a plastic time Q^ . 



When the parabolic profile, Eq. (1) is substituted in Eq, (13) 

 of Part II and one leta R-t* corresponding to a very large baffle, one ob- 

 tains for the pressure at the center of the plate. 



When t is less than 0j_ , the time required for the diffracted wave to travel 

 from the edge to the center of the plate, Eq, (3) reduces approximately to 



based upon geometrical acoustics. V.'hen "t is greater than ©^and the third 

 and higher time derivatives of z^can be neglected, a Taylor's expansion in 

 ©^ of the rightUP* side of Eq. (3) yields the "incompressive" approxima- 

 tion, 



b. xp«c<-;- -^Jililh ^ilUlo . (5) 



Unfortunately neither of the two limiting cases represented by Eqs. (4) and 

 (5) is entirely adequate to represent the facts in cases of practical inter- 

 est. Roughly, one may say that Eq. (4) holds in the initial phase of the 



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